The coat he wears looks very similar to the one Light was wearing when he died.
He walks up stairs to meet Ryuk, which could be seen as a subtle reference to Light's death.
The way he tosses the apple to Ryuk, as Light did when alive.
Light's red tie is wrapped around the shinigami's head.
The shinigami walks into a bright flash of light at the top of the stairs.
The fact that he inexplicably knows Ryuk's love for apples without asking the other Shinigami.
The fact that Ryuk says "Light" after the unnamed Shinigami leaves.
The same smile that Light shows upon mocking L's grave.
The red eyes that in the anime shows Light's 'Kira' personality.
He carries a scythe, similar to how Light does in some pieces of artwork.
The limp displayed while walking up the stairs is similar to the way Light limped out of the warehouse.
Light's "Kira smile" is shaped like his mouth.
The Unnamed Shinigami does not stay to hear the end of Ryuk's story. Yet he is very interested about the human world! If he is the reincarnation Light, he knows how the story ends and is upset about it and does not want to hear about it.
Another Clue is Light being seen in the shinigami realm in the end of opening 2.

After I found these I came to the conclusion that this shinigami must be Light in a reincarnated form.